Prior art is filled with numerous examples of pressure transducers. All diaphragm based pressure transducers have one thing in common, and that is converting an applied pressure into stresses in the plane of the diaphragm. These stresses can be conveniently measured and converted into an electrical signal by use of piezoresistive sensors which are mounted on or are part of the diaphragm. For instance, U.S. Pat. No. 3,800,264 entitled "HIGH TEMPERATURE TRANSDUCERS AND HOUSING INCLUDING FABRICATION METHODS", and U.S. Pat. No. 3,819,431 entitled "METHOD OF MAKING TRANSDUCERS EMPLOYING INTEGRAL PROTECTIVE COATINGS AND SUPPORTS" both issued to A. D. Kurtz et al. and assigned to Kulite Semiconductor Products, Inc., the assignee herein, demonstrate this principle. The most common arrangement is that of a clamped edge diaphragm wherein the outer portion of the diaphragm is fixed and the central region deflects under applied pressure. In this conventional device, the stress on the surface of the diaphragm varies from a maximum tensile stress at the clamped edges to a maximum compressive stress in the center of the diaphragm. The diaphragm can be made of metal, to which the sensors are cemented, or in the case of the cited patents, from a semiconductor material such as silicon on which the sensors are either embedded or affixed. For the cases where the diaphragm is silicon, one must recognize the fact that the piezoresistive effect varies with crystallographic orientation and in order to determine how the stresses are converted into resistance changes, the crystallographic properties of the piezoresistive coefficients must be taken into account.
Following the conventions introduced in an article entitled "SEMICONDUCTING STRESS TRANSDUCERS USING TRANSVERSE AND SHEAR PIEZORESISTANCE" by Pfann, et al. and appearing in the Journal of Applied Physics, Vol. 32, 1961, two distinct types of piezoresistive coefficients may be defined. These two piezoresistive coefficients are longitudinal and transverse. The longitudinal piezoresistive coefficient relates the relative resistance change due to an applied stress in a piezoresistive element when the stress is in the same direction as the current flow through the element. The transverse piezoresistive coefficient relates the relative resistance change due to an applied stress in a piezoresistive element when the stress is at right angles to the current flow through the elements. It should be noted that the transverse piezoresistive coefficient can be defined for a stress in the plane of the sensor as well as for a stress normal to that plane.
The operation of a piezoresistive pressure transducer can be broken down into three separate and simultaneously occurring phenomena. First, the diaphragm of the device converts the applied pressure into both surface and normal stresses. Second, the resistances of the piezoresistive elements (or "gauges" as they are referred to by those skilled in the art) are modified by these stresses, and third, the resistance changes of the gauges are converted into a single voltage change by a Wheatstone bridge circuit.
The various stresses that occur in a diaphragm due to an applied pressure can be obtained by applying conventional elastic theory using equations well known and commonly referred to in the art. For example, the amount of stress in a circular diaphragm transducer that is generated by an applied pressure will be worked out as follows:
For the normal stress (i.e., the stress perpendicular to the surface), the pressure-stress relationship is given by EQU .sigma..sub.z =-P (1)
and for surface stresses (i.e., the stresses parallel to the surface), the relationship is given by: ##EQU1## where .sigma..sub.z is the stress perpendicular to the surface, .sigma..sub.r is the stress in the radial direction which occurs at right angles to the clamped edge, P is the applied pressure, .alpha. is the radius of the circular diaphragm, T is the diaphragm thickness, .nu. is the Poisson's ratio, and r is the stress location. From equation (2), it is obvious that the maximum compressive (negative) stress occurs when r=0, which is located at the center of the diaphragm, and is given by: ##EQU2## wherein the ratio of .alpha./T is referred to as the aspect ratio of the diaphragm. The maximum tensile (positive) stress occurs when r=.alpha., which is at the clamped edge of the diaphragm and is given by: ##EQU3##
Along the diaphragm surface, the stress starts at this high positive stress level along the clamped edge, and then decreases until it reaches a maximum negative stress level in the center of the diaphragm.
For a square shaped diaphragm, the equations for the stress at the clamped edge and the center of the diaphragm are similar to those described above, except for the magnitude of the equation coefficients. The equations for a square shaped diaphragm are as follows: ##EQU4## wherein .sigma..sub.CX and .sigma..sub.CY are the X and Y direction surface stress at the diaphragm center, .sigma..sub.EX is the X direction stress at the clamped edge of the diaphragm, and .sigma..sub.EY is the Y direction stress at the clamped edge of the diaphragm.
The equations expressing normal and surface stresses having been established, the stress is next converted into a resistance change of the sensing elements by utilizing the piezoresistive effect. The governing equation for this resistance change is as follows: ##EQU5## In this equation, .DELTA.R is the change in gauge resistance under stress, which can be either a positive or negative change, R is the zero stress resistivity, .sigma. is the stress in the direction labeled by the subscript, and .pi. is the piezoresistive coefficient in the subscript labeled direction. Generally, for the most efficient operation of the transducer device, one longitudinal gauge may be placed at or near the clamped edge of the diaphragm and one placed at the center of the diaphragm, with the crystallographic axis of the gauges chosen such that a maximum longitudinal coefficient and a minimum transverse coefficient are realized, or in other words, these gauges will be sensitive to X direction surface stress and insensitive to Y direction surface stresses. Given this setup, an output voltage can then be generated in a Wheatstone bridge circuit (which utilizes four gauges), having a voltage equation given by: ##EQU6## wherein R.sub.1, R.sub.2, R.sub.3, and R.sub.4 are the zero stress gauge resistance values, .DELTA.R.sub.1, .DELTA.R.sub.2, .DELTA.R.sub.3, and .DELTA.R.sub.4 are the changes in gauge resistance with pressure, V.sub.In is the excitation voltage and V.sub.Out is the bridge output voltage. If the bridge is made from piezoresistors with the same zero stress value and the resistance change of each individual piezoresistor is equal in magnitude, but adjacent gauges have an opposite sign change, the equation becomes: ##EQU7##
A conventional low pressure (&lt;100 PSI) transducer is typically designed to have a full scale surface stress between 15,000 and 30,000 PSI so that the output voltage of the Wheatstone bridge is between 75 to 150 mV. A cross-sectional view of through a such a conventional prior art low pressure piezoresistive pressure transducer is depicted in FIG. 1A. The transducer assembly 10 consists of a carrier wafer 12 which may be fabricated from a semiconductor material, such as N-type silicon, and is preferably a single crystal structure. Such wafers are commercially available and are well known in the art. The wafer has a thin passivating dielectric oxide layer 14 on one surface and a glass or silicon supporting member 16 which is anodically or otherwise bonded to the other. A shallow depression 18 has been etched into the carrier wafer 12 and serves to define the diaphragm member 24 which has a deflecting region 28 and a non-deflecting region 29. The diaphragm has a vertical thickness 22 and a lateral dimension 21. Positioned above the diaphragm region 24 and bonded to the oxide layer 14 are the piezoresistive sensing elements 25 and 27. These sensing elements are designated outer sensing elements 25 and inner sensing elements 27 depending on their position in the device. The outer sensing elements 25 are positioned above the clamped edge of the diaphragm, while the inner sensing elements 27 are positioned near the center of the diaphragm. The outer sensing elements 25, because they are under tension at low pressures, exhibit a positive change in resistance, and the inner sensing elements 27, because they are under compression at these pressures, exhibit a negative change in resistance. The sensing elements 25 and 27 are typically fabricated from highly doped P+ monocrystalline semiconductor material and may be shaped in very intricate patterns.
The magnitude of the stresses across the diaphragm surface of the device depicted in FIG. 1A is graphically depicted in FIG. 1B. The analysis performed to generate the stress profiles shown in this figure and in all other graphs to be shown was accomplished using a finite element analysis program which subdivides the system into small segments and solves them simultaneously. Such programs produce highly accurate results and are well known to those versed in the art. This analytical method was chosen over a theoretical one due to the difficulty in obtaining accurate closed form solutions for the systems in question. According to the graph depicted in FIG. 1B, the X axis represents a distance (measured from the edge of the device to its center) and the Y axis represents a stress (either tensile or compressive) exhibited by the transducer's top surface at the given distance. The upper curve 34 corresponds to measurements of surface stresses as one tracks from left to right across the device. The curve reaches a maximum value 35 at a point where the tensile stress is the greatest and a minimum value 33 where the compressive stress is the greatest. The lower curve 37 is a measurement of the applied pressure normal to the surface of the device, and is near zero relative to the resulting surface stresses as displayed on the graph. A typical case would have a full scale surface stress of 20,000 PSI and thus require an .alpha./T ratio of approximately 20. For transducers designed to operate at lower pressures, a higher .alpha./T ratio is required. For transducers designed to operate at higher pressures, a lower .alpha./T ratio is required.
At both high and low values of this .alpha./T ratio, a mechanical non-linearity between the applied pressure and the surface stresses occurs. This non-linearity can be overcome by increasing the efficiency of the applied pressure to surface stress conversion. This increase in efficiency has been demonstrated in an improved low pressure traducer design which allows the fabrication of high output, low pressure sensors with substantially linear outputs. The device is described in U.S. Pat. No. 4,236,137 entitled "SEMICONDUCTOR TRANSDUCERS EMPLOYING FLEXURE FRAMES" issued to Anthony D. Kurtz et al., and assigned to Kulite Semiconductor Products, Inc., the assignee herein. A cross-sectional schematic diagram of the device 20 is depicted in FIG. 2A. The transducer pictured therein has essentially all of the same features of the device depicted in FIG. 1A, but differs in that it employs a thick central boss 23. This thick central boss 23 operates to improve the stiffness of the deflecting diaphragm member 24 thus allowing it to achieve a large output while avoiding the problem of undue diaphragm stresses. In this design, the maximum tensile surface stress still occurs at the clamped edge of the diaphragm, but the maximum compressive stress now occurs at the edge of the boss.
The magnitude of the stresses across the bossed diaphragm surface of the device depicted in FIG. 2A is graphically depicted in FIG. 2B. As in the graph depicted in FIG. 1B, the axes are stress versus distance. The upper curve 30 corresponds to measurements of surface stresses as one tracks from left to right across the device. The curve reaches a maximum value 36 at a point where the tensile stress is the greatest and a minimum value 38 where the compressive stress is the greatest. The lower curve 32 is a measurement of the applied pressure normal to the surface of the device, and is near zero relative to the resulting surface stresses as displayed on the graph.
For extremely high pressures (&gt;20000 PSI), the .alpha./T ratio is close to one, and not even the bossed diaphragm design remains valid. FIG. 3 demonstrates such a case. As in the previously discussed graphs, the axes in FIG. 3 are stress versus distance. Notice should be taken of the fact that this graph differs significantly from those depicted in FIGS. 1B and 2B. Specifically, since the device is operated at a high pressure, there is a net compressive stress and there is no longer a point of positive (tensile) stress. Therefore, the top of the Y axis on this series of graphs (and not its center) represents the zero point stress region. The upper curve 80 corresponds to measurements of surface stresses as one tracks from left to right across the device. The curve reaches a maximum value 84 at a point where the compressive stress is the least, and a minimum value 85 where the compressive stress is the greatest. The lower curve 82 is a measurement of the applied pressure normal to the surface of the device, and, as mentioned above, is not near zero as it was in the prior art low pressure transducer devices. It is here where current methodology is shown to be lacking as there is currently no way to form a gauge with a positive resistance change. This inability to create negatively and positively changing gauges for inclusion into the Wheatstone bridge circuit causes the bridge to exhibit an electrical non-linearity of applied pressure to output voltage which results in a defective transducer design.
It is, however, possible by appropriate choice of crystallographic orientation for the gauges and by taking into account the crystallographic dependencies of the piezoresistive coefficients for the case of high normal pressure stress to obtain positive changes in resistance. Comparison of FIGS. 2B and 3 shows that for the conventional low pressure design, the normal stress is negligible when compared to the surface stresses, but for the high pressure transducer, the normal stress is of the same order of magnitude as the surface stresses. This property can be exploited in the design of an improved high pressure transducer.
It is therefore a primary objective of the present invention to provide a piezoresistive pressure transducer which is capable of operating at pressures in excess of 20000 psi without the diminished output experienced by prior art piezoresistive transducers and that does not experience the non-linear pressure versus stress behavior found in these prior art devices.